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An hp-Discontinuous Galerkin Method for the Optimal Control Problem of Laser Surface Hardening of Steel

Gupta Nupur, Nataraj Neela (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, we discuss an hp-discontinuous Galerkin finite element method (hp-DGFEM) for the laser surface hardening of steel, which is a constrained optimal control problem governed by a system of differential equations, consisting of an ordinary differential equation for austenite formation and a semi-linear parabolic differential equation for temperature evolution. The space discretization of the state variable is done using an hp-DGFEM, time and control discretizations are based on a discontinuous Galerkin...

An hp-Discontinuous Galerkin Method for the Optimal Control Problem of Laser Surface Hardening of Steel

Gupta Nupur, Nataraj Neela (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

An ill-posed nonlocal two-point problem for systems of partial differential equations.

Il'kiv, V.S., Ptashnik, B.I. (2005)

Sibirskij Matematicheskij Zhurnal

An implementation of recursive quadratic programming variable metric methods for linearly constrained nonlinear minimax approximation

Ladislav Lukšan (1985)

Kybernetika

An implicit extragradient method for hierarchical variational inequalities.

Yao, Yonghong, Liou, Yeong Cheng (2011)

Fixed Point Theory and Applications [electronic only]

An implicit hierarchical fixed-point approach to general variational inequalities in Hilbert spaces.

Zeng, L.C., Wen, Ching-Feng, Yao, J.C. (2011)

Fixed Point Theory and Applications [electronic only]

An implicit iterative scheme for an infinite countable family of asymptotically nonexpansive mappings in Banach spaces.

Wang, Shenghua, Yu, Lanxiang, Guo, Baohua (2008)

Fixed Point Theory and Applications [electronic only]

An implicit-function theorem for a class of monotone generalized equations

Walter Alt, Iosif Kolumbán (1993)

Kybernetika

An impulsive control problem with state constraint

P. L. Lions, B. Perthame (1989)

Annales de l'I.H.P. Analyse non linéaire

An index formula for the degree of (S) $_{+}$ -mappings associated with one-dimensional $p$ -Laplacian.

Kobayashi, Jun, Ôtani, Mitsuharu (2004)

Abstract and Applied Analysis

An inexact proximal-type method for the generalized variational inequality in Banach spaces.

Ceng, L.C., Mastroeni, G., Yao, J.C. (2007)

Journal of Inequalities and Applications [electronic only]

An intermediate existence theory in the calculus of variations

Frank H. Clarke, Philip D. Loewen (1989)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

An interpolatory estimate for the UMD-valued directional Haar projection [Book]

Richard Lechner (2014)

An intersection theorem for set-valued mappings

Ravi P. Agarwal, Mircea Balaj, Donal O'Regan (2013)

Applications of Mathematics

Given a nonempty convex set $X$ in a locally convex Hausdorff topological vector space, a nonempty set $Y$ and two set-valued mappings $T : X ⇉ X$ , $S : Y ⇉ X$ we prove that under suitable conditions one can find an $x \in X$ which is simultaneously a fixed point for $T$ and a common point for the family of values of $S$ . Applying our intersection theorem we establish a common fixed point theorem, a saddle point theorem, as well as existence results for the solutions of some equilibrium and complementarity problems.